Give some examples of everyday vibrating objectsavv,zmv 7y uzctkvep2t9:bzw38+ 32i. Which exhibit SHM, at least appy+ m:2k vvv3wtctbu p8eizvz2, 3a 79zroximately?

Is the acceleration of a simple harmonic oscillq6:fc*j2 cxfp( wxx/z ator ever zero? If so, where?

Explain why the motion orxb td2 (9vwwmuv*51uz rd9max tx92 7f a piston in an automobile engine is approximately simple ha9dab9m1xr d zxxt( v7urwu 5*v9m2w2trmonic.

Real springs have mass. Will the true pe 6.k- id by vuijcb0*5hrol97eriod and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized masli. b -ky*j60oihevb9 5u 7rcdsless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillator (0j)7/,xffr yk ut(r gfSHO)?

A 5.0-kg trout is attached to the hook ofjhqc77/yzl)hf j2e2.dsh6 hy a vertical spring scale, and then is released. Describe the scale readinghlj)7qhzde 27y2c./6s fhj yh as a function of time.

If a pendulum clock is accurate at sea level, will it ga)f8uupm 1: vz6bt-u 8h1kd qqdin or lose time when taken to high alti8fu:u8u11d hk z t )-vmdpb6qqtude? Why?

A tire swing hanging from a branch reaches nearly toj.,ej *zxwqu2, gm2ln0 a4ngx the ground (Fig. 11–48). How could you estimate the height of the branch using only a stopwatch?g,xq,waj 2ge4zum * n.0jl2xn

Why can you make water slosh back and forth in a pan only if yo,9esh s.,xjc 9jck58dhaka1t u shake the pan at a certain 85 9jejx 1 ctksshkcd,9h.a,afrequency?

Give several everyday examples of resoujc5ofefgf56 o 54rtrg n6+)wnance.

Is a rattle in a car ever a resonance pheq,a*ueipm)(rve yp ,i8x2sz+nomenon? Explain.

Is the frequency of a 2zipj-tr f ,*dt +3*x flr/hgmh1adm 0simple periodic wave equal to the frequency of its source? Why or1,tj*h 3/d 2a g zrfpd0 -f+t*ixhlrmm why not?

Explain the difference between the speed of a transveztgc4c f5(/ byv,nyd v*i :y1drse wave traveling down a cord and the speed of a tiny piece of the cord.5dz * 4dvn/cg(,byyvi :cy1ft

Why do the strings used for the lowest-frequency notes odtwlu+ z p gm4i4mx -g7jy8x 2nb9qn+0n a piano normally have wire wrapped around tbip0xq9t8n4xgj +4myul gndw2-z 7+mhem?

What kind of waves do you thinp;vf/4 iqvnw0x kxd(vauy wx:c/;,0nk will travel down a horizontal metal rod if you strike ityc vxvv idwk:0 f(an/ /4 0,qwxu;;npxs end (a) vertically from above and (b) horizontally parallel to its length?

Since the density of air decreases with an incr:s4mi s.yn*msease in temperature, but the bulk modulus B is nearly independent of temperature, how would you expecny:i .*msms 4st the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amplitj,,z 5ztl8e*+4 uni 6fxxxm bpude as they travel away from tml6xtu n8z+ fze,j5 4b* ixp,xhe source.

Two linear waves have the same amplitude and speed, and otherwise are ident; siwcts/m9xix; za d4v8d62v ical, except one has half the wavelength of the other. Wh6azsvi8vx/ix9;wd 4tm sc2d;ich transmits more energy? By what factor?

When a sinusoidal wave crosses the bkmf9evia9ps9mf 2 q2 :oundary between two sections of cord as in Fig. 11–33, the frequenev:fi9 9kp2mm2q9asf cy does not change (although the wavelength and velocity do change). Explain why.

If a string is vibrating in three se w e 0zd+as(he-()vgtay:)fqygments, are there any places you could touch it with a knife blade without di:(-yeg(da zq0h ) e)yta+s wvfsturbing the motion?

When a standing wave exists on a string, the ei*e0l9er/b gr4v 4ci3ebyw 3vibrations of incident and reflected waves cancel at the nodes. Does this mean that energy was destroyedve igir y 0/eerw*44c9b 33elb? Explain.

If we knew that energy was being transmitted from one p qkwr.c lf:b/(lace to another, how might we determik/ .lrw cfb(:qne whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with a.dp8v:gddwfey qb 2wi z44c6 1mplitude 0.18 m, what is the total distance it travels in one peyc.4 14vewp 28 bzgdwifqd:d 6riod?    m

  An elastic cord is 65 cm long when a weight off:3k.m. ziqyd 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What is the “spring” constant k of this elastic cyid .f.qz 3:mkord?    N/m

  The springs of a 1500-kg car compressq3.-(ivjtubo 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequeovt-jb. (i u3qncy of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish 9oqae37om5o-,*qyb *fxki,up0yd ij hangs from it. (a) What is the spring stiffness const0ox j*5dfuiyo,*qo9 pe3qy,amik- 7b ant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a muql.nmtlou xq2z -63,:lro; v ass of 0.60 kg is hung from it. m-lqulr;tl .3:zn2,xqo6 uv oWhat is its frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position h3/ -bzex 3wwe hx6 eh;j;-qdkx of the mass in Fig. 11–2 at times t = 0,t =dw wx3jqkezh3-bheeh; /x-; 6 $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spider’s web. The web vt2miyxwxk/5 6ibrates predominatelymx x62 /wkit5y with a frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequencymx;k1i c81t lv of 0.88 Hz. When an additional 680-g mass is added to m, the frequency is 0.60 Hz. What is thxi t1c1 ml8v;ke value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.0 times per second with an am) iu)5zeyr4,k xn kr s:se2w.rplitude of 0.13 m.s uk.:yxr)z,r2 w e snki54er) Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibriu1l si091 ewr)h1punuem is the speed of a SHO half the maximum value whsnlu1r0 )pee1 19ui?$\approx$    A

A mass attached to the end of a spring is stg-gd2 ykk1x y b3pd:/bh; jd6aretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 06ortzk sxh ml.;0sc(dr333 jy.315 m. If the spring is stretched an additional 0.130 m and released, how long does it take to reach the (new) equilibrium position agdzom.h306r ( yjtkcx sls33r;ain?    s

  An object with mass 3.0 kg is attached to a spring with +gja0j/ 5v ;yp (qok/hnmrby 6spring stiffness constant k = 280 /(65om a ygp;hn rj0k+vyqj/ bN/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the sprsw.:i1 hvkp3hv,div nh3v /g3ing of a toy popgun 0.200 m to “load” a 0.180-kg ball. With what speed will the ball leave 3d/ pi:vih ,hwn31vh3 .kvgvsthe gun?    m/s

  A mass sitting on a horizontal, frictionless surface i4e+ j1c8s u7iv5u gimps attached to one end of a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring comprv4jcu 8iisu e57mp+1g essed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the eq bfmifnjwedhg-u-8,)u 9(do.uation x = 0.45cos6.4t where x is in meters and t is in sed)edo 9u.b8--wjf m(ug,h ifn conds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equ3x3fj a 2amav4ilibrium is the energy of a SHO half KE and half PE a32xjmvf 4a3a? ±    A

  If one vibration has 7.0 times the energy of a second, but their fzlx,l1p ;.5)p ufk amnrequencies and masses are the same, what is the ratio of their amplitudes? 1lufpm 5kzlx.,;p n)a   

  A 2.00-kg pumpkin oscillates from a vertically hanging light spr 1t uu.yvllbu9dfw0y.*lg7 2ging once every 0.65 s. .l *gf2y 0.7luuvuylbgt9dw1
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported by two identical parallel vertical springs, eavh: bpu fon:6v)5mg8lch with spring stiffnes b5ogvl hpmu6fv:)n: 8s constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equationsgv,p5pk;wqg. q 4 dc9 zcx)3n x = 0.38sin6.5t where x is in meters and t i,xn)3zpc v w5cgp4; qgsq9.d ks in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, labeled A and B. For q1e loa p4+lfx ho)3a/6d4fsieach, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on the end of a horizontalr fp919; mdsst spring (k = 124 N/m) is struck by a hammer, which gimstsf 9d;9r1 pves the mass an initial speed of 2.96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with sq qp/z gnoygxjt . wh791-/px+/6ijrspring stiffness constant 305 N/m vibrates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes / tq+h1 -zn/9roys/xj.wipgq6 gx7jpthrough the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring stiffnd61g -g1/g jktr2qi gress constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikesuk 3dq,; 6rmlo5hlkp;l lg)6a gcs0t) a 0.600-kg block attached to a fixed horizontal spring whose spring stiffness6uql5tl g0;kh, lgsm6cpold)3 ka r); constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kv5c 5yru. uh*rg jumps from a high bridge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungeuyv c55 hr*.ure cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exajas* sa 6+v/ca*wzh;wctly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to mho.)sz* ,qt ewn.sgx+ake exactly one swing per second? (That is, one complete vibration takz ,n.).ewg+x* qssthoes exactly 2.0 s.)    m

  A pendulum has a period x e*;gwpqz ,b,of 0.80 s on Earth. What is its period on Mars, where the ac*bgpz,qw e;x,celeration of gravity is about 0.37 that on Earth?    s

  What is the period of a si, n3 vt-hjbj*9 binfd3mple pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum ix+jc3n*t3xqpd8f2 lz s 0.760 m, the pendulum bob has a mass of 365 grams, a xtl+j d3zp2f*x3ncq8nd it is released at an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.+ t2jbf4wg(nye6tgya/ i9p /ka z4n 6c9930 m. If the clock loses half a minute per day, how should you adjust tgpg9/e aa i4nz 6(wjc42ybf y/t6n+tkhe length of the pendulum? shortened by    mm.

Derive a formula for the maximumrnok8 vrbcr.if 0fz bp.f av:779*.vo speed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a freq4(2c2pnjlbhy uency of 2.5 Hz. At it is released from rest starting at an anglp2h ync4blj( 2e of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave cr;zq+cfg yn ea6q+jjoc+0fw 5*fa4 .qdests pass the bow of his anchored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the wa60qjwn+fzoge;yqj+dcf+* a.c 5 q 4f aves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a spf0uc. xy69ky xyt7 d6deed of 343 m/s How far apart are the wave xx6kd t9cdy .607uy yfcrests (compressions)?    m

  (a) AM radio signals have frequencies between 550 kHz and 1600 kHz (kilohertz;72wtvs - jgmr) and tra2vgrm ws7jt-;vel with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal waves i( pc c/-ba6*+qpw) 4wfozsasdn
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elastic modulus, )+(9sg c iugqtbut one is twice as dense as the other. In which rod will the speed of longitudinal waves be greater, and by what factor? gg9 s (q)iu+tc  

  A cord of mass 0.65 kg is stretched between two supports (ncyu )r.c/k;h3f2cawx, v rp3h h7e o28 m apart. If the tension in the cord is 150 N, how long will it take a pulse to travel from one support to tha(ch,v.)w/;c 2ey x f3 rhrocphnk73 ue other?    s

  A ski gondola is connected toy8)98j - w1z vzqf*wla5ts yqa the top of a hill by a steel cable of length 620 m and 9wqyt az1-8 vsqa5y8 )lfjzw* diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side of his ship just below;z iuckw eq1 -r+v5fw; the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly brwiz qfwv+15;eu kc-;elow 3.0 s later. How deep is the ocean at this point?    m

  P and S waves from an earthquake travel at different speeds, and th0 zivei ; 32-pfy4j+ vvt5lchxis difference helps in locating the 0 i-vvpi5y f2xjc3zth; l4+evearthquake “epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can betz)u f 3yf 7ib2ms52uv approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical ofu73sbm5 f2)zfy2uvit earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplita0mvw/ jtj/2m9kl/r 2 3eej vhudes, of an earthquake P wave passing through the Earth and detected at two points 10 km a/2kmetj ma9ew3j0h j2/ vlvr /nd 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is measured to b7qk*v*c ra*op e q*pcra* 7 o*kv$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of elhbo f g(:b:-the same frequency travel through the same portion of the Earth, but one is carrying twice the energy. What is the ratio of the amplitude( b fh:g:lbeo-s of the two waves?   

  Two waves traveling along a stretched strin;dy+np:( +bimh dg,dfg have the same frequency, but one transports three times the power of the other. What is the ratio of++pdn ,d(di f:yhbm ;g the amplitudes of the two waves?   

  A bug on the surface of a pond is observed to move up and down a t)0-epl8pnm bm zo l)d6loip8/ro40ho otal vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the buoomh6op0d-4pe0ni)/b)m8l l8pz o lr g’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. (a) Sketch th4r8aswrjh( xag0l/b39 dy8 /8ie:riufxf n v:e shape of the string at the moment they directly overlap. (b) Sketch the shape of the strighxrnval j4a(8:yu9er3fwi0 8ib/ 8xds: r /fng a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz as its fuka8m/+ixdcks5w6okak,1 q+ wndamental frequency, what are the frequen8k/6dkk1o++wk sq5i wa cma,xcies of the first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingcoq s4+z; qs- yt7w)eqered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the st+ qwqc7t)s qoz;yes4-ring vibrates as a standing wave.)    Hz

  A particular string resonates + svo:vx5nlb1sg-m) fvsj3(0hgxa vx6)+li f in four loops at a frequency of 280 Hz. Name at least three other frequencies at which it will resonate. bs 3h)i fo+ jvvsxsgl)(n+-:axvvmf065l1xg$f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the fr v h5.ziki hrj,4 h2i;d1,c6g.sjii rai6(ji yequency of standing waves is 475 Hz, how far apart are two adjaczi6 j1 ,kci4 vijihryri;s(5i. hdi, gh.2aj6ent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, whp3l, c7cobdo /cq0i ,funy:*x at is the frequency of the fundamencq/ l:,uyipcb7,3*nc 0odoxftal?    Hz

  A guitar string is 90 cm long and has a mass a4ai+pr6j *zvx24vhpof 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is undp2 r6a *aji+z 44vhpvxer a tension of 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar str l9bh*kre-k:,x z; p8sz+kb tcing is supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct tzk- ckpr +b*,ks9e:h8;txlb z he frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is suppose dsb 5v(ec+u2hd;l ;*2t wyf4q)xb ctvd to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent shoul2 dbs+*5b yq wet vhx)dvcc 4fl(;u2;td the tension in the string be changed to correct the frequency? decreased by    %

  One end of a horizontal string is attacjb7 e2db96 a hu8r7 rgejb,k(phed to a small-amplitude mechanical 60-Hz vibrator. The string’s mass perbd2b9 8p7ka (bjrg7hu6re,ej unit length is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the stsuxc m2:n; hblbz,x x ,j63lkv97o o*sring may be adjusted by moving the pulley. If the hanging mass m is x,zs7 cxs n vo3h o;jl2u *6lb:,k9mbxfixed at 0.080 kg, how many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the water backt7i27v3 nsiqkfqlt2or82p9i and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hz. Wi2q27o 3ti ln9k8t v2pr7qsifhat is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strikes a4a.t wper9 g0n*y1 2tncnxd3y boundary within the Earth between two kinds of material. If it approaches the axw2*y9ery0n3.gt4nn cp td1boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” npr5;qnpt 34owrht3;where the velocity changes from 2.8 m/s to 2.1 m/s If the inct t;n; r4pp335 qrhnowident wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when idlqw5vo00u2vd. lm 2jt hits a layer of cold, dense air. If the sound wave hits the cold air interface v05l2udlom2.j0q vw d at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave iu0pv3qb)d v hnv)bg5wt+(k0strikes a boundary between two types of rock at a 3w0v 5 vb+hq 0(bdnutv) k)pgi38 $^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diametpppcp/d4 nkpo8/76h5p6fqrwgc y1h 9 m6eg7 rer. According to the user’s manual, the depkhycfm1rdp c7 7pwho6n pp59 r46/g/p6q8 gish has to be pointed in the direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 qr51u;);yu ibazmxz1i sb(r+ 4bl9t-1sw lmzkm and velocity 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted tbl iuq zw-11bzasmlx9brtuy1)r s( +z5m; 4i;o the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant of 550 kN//l* qnree4x q.m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (approximately 5 mi/h). [Hint: Use conservation of enerq* r/nx l4qee.gy.]    m

  A 65-kg person jumps from a window to a fire net 18 m belowv7 lh,cc t3xjh:s24 fe, which stretches the net 1.1 m. Assume that the net behaves like a simpxhs72v4jc c:l3ef ,htle spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the mvq 5 ae/ezp-zcbf80f j/g):hend of a freely hanging spring. The mass then falls 33 cm before izma-ebhf05ve 8pz :)/fg cj /qt stops and begins to rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 m/s (Fig. 11–54), compremp eo4db2d/opa4 .8fk ssing the spring 5.0 m. (a) What is the spring stiffness constant of the spring? 2ofpdoep8dk.bam4/ 4    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (8p8s byc(0qtd7 w5mwkdiameter 8 cm) at just the right pace of about 1 step per second, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the co7pws b(d8cq8 tkm0wy5ffee.    cm/s

  The ripples in a certain groove 10.8 cm frocy , , eh2 ,bf*l;fgv+h*qssqvm the center of a 33-rpm phonograph record have a wavelenvvhhq e s,,bf; s+c 2lgq*,yf*gth of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0.650cos7.40t where xut:uhxg,l(o-x3x ,p gac8h ; r is in meters l gro 8 (uxh;,xa,u txp:g-ch3and t in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillatey;d1uqzsdyfd l1)sen):p /t9 s with frequency f. What is its frequency if it acceler zy/ q9eyddlpf;dss)t1) 1:nuates at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg m 8hdi+0 uxsx 2qs:p:av ,:d qhlb8rmx9an stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a while :,disrxd +bmv29s:hhp:u8xx8al 0qq.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instru csha.sz9 5 p0p5tr aom5*d/ibment are tuned to play at 392 Hz (G) and 440 Hz (Ats5r/5p9 pb*d0 mchoia .a5zs).
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched two-part cord of Fig. 11–30y,bpjalcb wz0ne;4c.n/u( 4y1qew m3. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the liwn0 /e pzcmu y4wy.,eql1bb ;ac 0j(4nghter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibratevw+ 6x+9nrc/quki,m+l ; vz zlb h0vd4s at a frequency of 264 Hz, and the tip of each prong moves 1.8 mm to either side of center. C6hvu 4rlnv cl+b0m+v;z, wxiq/9 +zdk alculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple 3k2ac)kqz i a-k8xvczjta2 3, harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose kz-)q2aic3tzv8kj 2k, a xa3ccontact with the board during the oscillation?

A string can have a “free” end if that end is attached to a ring that can8*dbftsn0jvm;, qq yde7tp64sb qh3 , slide without friction on a ver bh*v 63byptj7q fstnmsqd80,e4,;qdtical pole (Fig. 11–57). Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way swing tx. nv.jra8( i crm8a*jakes 1.000 s. a8r j..m8xnirjv(a c *
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the +v6asa,c/zj (af1nj svertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vc1a +6san,aszf/vj (j ertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

  A block with mass $M=5.0\mathrm{kg}$ rests on a frictionless table and is attached by a horizontal spring $\begin{pmatrix}k=130\mathrm{N/m}\end{pmatrix}$ to a wall. A second block, of mass $m=1.25\mathrm{kg}$ rests on top of M. The coefficient of static friction between the two blocks is 0.30. What is the maximum possible amplitude of oscillation such that m will not slip off M?    m

  A 10.0-m-long wire of mass 123 g is stretched under a bcz0u /zcm,)bnk+9qp jzz 0-.cez-butension of 255 N. A pulse is generated at one end, and 20.0 ms later a second zb9kuzczn.z,j0p+z c bmc que -0)b/ -pulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a-*qz w2 bz1kyf spring with spring stiffness constant k. A penny of mass m is placed on top of the bl-1w b zfk*yzq2ock. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 120 c)l5 dz5nj1*gck6arf0-kg car at the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? ackdln )j5f z*1rg65c [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as show1cir7 -gp-x: 5sk zotgv4 huqokp7 z :44qib0tn in Fig. 11–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimrhu4o4 -:4-0kzp tz5ibk7iq g1x :svpgt qo7cate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz